Matrix interpretations are widely used in automated complexity analysis. For these interpretations, certification boils down to determining the growth rate of A^n for a fixed non-negative real matrix A.Since the direct approach to compute the growth rate of A via algebraic numbers is quite slow, in this work we formalize the Perron-Frobenius theorem: it permits us to avoid algebraic numbers, so that our new certification algorithm only has to perform simple arithmetic operations. To cover the theorem in its full extend, we further establish a connection between two different Isabelle/HOL libraries on matrices, which enables an easy exchange of theorems between both libraries.
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